Novel Conditions on the Non-Normal Cayley Graphs of Valency Six

Mahtab Hashemian and Mehdi Alaeiyan

doi:10.17485/ijst/2015/v8i16/56650

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Novel Conditions on the Non-Normal Cayley Graphs of Valency Six

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Indian Journal of Science and Technology

DOI: 10.17485/ijst/2015/v8i16/56650

Year: 2015, Volume: 8, Issue: 16, Pages: 1-4

Original Article

Novel Conditions on the Non-Normal Cayley Graphs of Valency Six

Mahtab Hashemian and Mehdi Alaeiyan^*

Department of Mathematics, Karaj Branch, Islamic Azad University, Karaj, Iran; [email protected]

This work is licensed under a Creative Commons Attribution 4.0 International License.

Abstract

A Cayley graph X = Cay(G, S) on a group G is said to be normal if the right regular representation R(G) of G is normal in the full automorphism group Aut(X). In this paper, two novel conditions are outlined to identify the non-normal Cayley graphs of valency six. As an application, some non-normal Cayley graphs of valency six on A₆ and A₅ are obtained.
Keywords: Automorphism Groups, Cayley Graph, Normal Cayley Graph